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<b>QuantLib</b>::<a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html">StochasticProcess1D</a></div>
<h1>StochasticProcess1D Class Reference</h1><!-- doxytag: class="QuantLib::StochasticProcess1D" --><!-- doxytag: inherits="QuantLib::StochasticProcess" --><code>#include <ql/stochasticprocess.hpp></code>
<p>
Inheritance diagram for StochasticProcess1D:<p><center><img src="class_quant_lib_1_1_stochastic_process1_d__inherit__graph.png" border="0" usemap="#_stochastic_process1_d__inherit__map" alt="Inheritance graph"></center>
<map name="_stochastic_process1_d__inherit__map">
<area href="class_quant_lib_1_1_forward_measure_process1_d.html" shape="rect" coords="434,6,636,30" alt="">
<area href="class_quant_lib_1_1_generalized_black_scholes_process.html" shape="rect" coords="414,54,656,78" alt="">
<area href="class_quant_lib_1_1_geometric_brownian_motion_process.html" shape="rect" coords="410,102,660,126" alt="">
<area href="class_quant_lib_1_1_hull_white_process.html" shape="rect" coords="466,150,604,174" alt="">
<area href="class_quant_lib_1_1_merton76_process.html" shape="rect" coords="467,198,603,222" alt="">
<area href="class_quant_lib_1_1_ornstein_uhlenbeck_process.html" shape="rect" coords="435,246,635,270" alt="">
<area href="class_quant_lib_1_1_square_root_process.html" shape="rect" coords="460,294,610,318" alt="">
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</map>
<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center><a href="class_quant_lib_1_1_stochastic_process1_d-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
1-dimensional stochastic process
<p>
This class describes a stochastic process governed by <p class="formulaDsp">
<img class="formulaDsp" alt="\[ dx_t = \mu(t, x_t)dt + \sigma(t, x_t)dW_t. \]" src="form_241.png">
<p>
<p>
<table border="0" cellpadding="0" cellspacing="0">
<tr><td></td></tr>
<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
<tr><td colspan="2"><div class="groupHeader">1-D stochastic process interface</div></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="25203cac75731710eb4902823065b095"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::x0" ref="25203cac75731710eb4902823065b095" args="() const=0" -->
virtual Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#25203cac75731710eb4902823065b095">x0</a> () const=0</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the initial value of the state variable <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e06f30a6c4425e8c3e4633d1cf15c761"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::drift" ref="e06f30a6c4425e8c3e4633d1cf15c761" args="(Time t, Real x) const=0" -->
virtual Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#e06f30a6c4425e8c3e4633d1cf15c761">drift</a> (Time t, Real x) const=0</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the drift part of the equation, i.e. <img class="formulaInl" alt="$ \mu(t, x_t) $" src="form_251.png"> <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9df3a04e3fab76cdee05ab834d5b7cb3"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::diffusion" ref="9df3a04e3fab76cdee05ab834d5b7cb3" args="(Time t, Real x) const=0" -->
virtual Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#9df3a04e3fab76cdee05ab834d5b7cb3">diffusion</a> (Time t, Real x) const=0</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the diffusion part of the equation, i.e. <img class="formulaInl" alt="$ \sigma(t, x_t) $" src="form_252.png"> <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#ee564ee8adf46c50265cd990b1dcd8a3">expectation</a> (Time t0, Real x0, Time dt) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#bb8a7016bec7d28872df221fb8995853">stdDeviation</a> (Time t0, Real x0, Time dt) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#5e92435fcc5c43be09e627494cf7a9d0">variance</a> (Time t0, Real x0, Time dt) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#096b196eb0c6e453acbd428ae378c7de">evolve</a> (Time t0, Real x0, Time dt, Real dw) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#6c8e95cb5b48a9ca86fef990c92c58c9">apply</a> (Real x0, Real dx) const</td></tr>
<tr><td colspan="2"><br><h2>Protected Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="704996c48f48a23c4db6a6549a094807"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::StochasticProcess1D" ref="704996c48f48a23c4db6a6549a094807" args="(const boost::shared_ptr< discretization > &)" -->
</td><td class="memItemRight" valign="bottom"><b>StochasticProcess1D</b> (const boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_stochastic_process1_d_1_1discretization.html">discretization</a> > &)</td></tr>
<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ea3658beebc66268a48cf5273cce6abd"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::discretization_" ref="ea3658beebc66268a48cf5273cce6abd" args="" -->
boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_stochastic_process1_d_1_1discretization.html">discretization</a> > </td><td class="memItemRight" valign="bottom"><b>discretization_</b></td></tr>
<tr><td colspan="2"><br><h2>Classes</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">class </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_stochastic_process1_d_1_1discretization.html">discretization</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">discretization of a 1-D stochastic process <a href="class_quant_lib_1_1_stochastic_process1_d_1_1discretization.html#_details">More...</a><br></td></tr>
</table>
<hr><h2>Member Function Documentation</h2>
<a class="anchor" name="ee564ee8adf46c50265cd990b1dcd8a3"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::expectation" ref="ee564ee8adf46c50265cd990b1dcd8a3" args="(Time t0, Real x0, Time dt) const" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">virtual Real expectation </td>
<td>(</td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>t0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Real </td>
<td class="paramname"> <em>x0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>dt</em></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const<code> [virtual]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>
returns the expectation <img class="formulaInl" alt="$ E(x_{t_0 + \Delta t} | x_{t_0} = x_0) $" src="form_253.png"> of the process after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_245.png"> according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
<p>
Reimplemented in <a class="el" href="class_quant_lib_1_1_hull_white_process.html#f718d7a907863b462830ca96dda4321c">HullWhiteProcess</a>, <a class="el" href="class_quant_lib_1_1_hull_white_forward_process.html#f718d7a907863b462830ca96dda4321c">HullWhiteForwardProcess</a>, and <a class="el" href="class_quant_lib_1_1_ornstein_uhlenbeck_process.html#f718d7a907863b462830ca96dda4321c">OrnsteinUhlenbeckProcess</a>.
</div>
</div><p>
<a class="anchor" name="bb8a7016bec7d28872df221fb8995853"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::stdDeviation" ref="bb8a7016bec7d28872df221fb8995853" args="(Time t0, Real x0, Time dt) const" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">virtual Real stdDeviation </td>
<td>(</td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>t0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Real </td>
<td class="paramname"> <em>x0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>dt</em></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const<code> [virtual]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>
returns the standard deviation <img class="formulaInl" alt="$ S(x_{t_0 + \Delta t} | x_{t_0} = x_0) $" src="form_254.png"> of the process after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_245.png"> according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
<p>
Reimplemented in <a class="el" href="class_quant_lib_1_1_hull_white_process.html#c731332c432f5be07edc3bda917e6ea0">HullWhiteProcess</a>, <a class="el" href="class_quant_lib_1_1_hull_white_forward_process.html#c731332c432f5be07edc3bda917e6ea0">HullWhiteForwardProcess</a>, and <a class="el" href="class_quant_lib_1_1_ornstein_uhlenbeck_process.html#c731332c432f5be07edc3bda917e6ea0">OrnsteinUhlenbeckProcess</a>.
</div>
</div><p>
<a class="anchor" name="5e92435fcc5c43be09e627494cf7a9d0"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::variance" ref="5e92435fcc5c43be09e627494cf7a9d0" args="(Time t0, Real x0, Time dt) const" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">virtual Real variance </td>
<td>(</td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>t0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Real </td>
<td class="paramname"> <em>x0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>dt</em></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const<code> [virtual]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>
returns the variance <img class="formulaInl" alt="$ V(x_{t_0 + \Delta t} | x_{t_0} = x_0) $" src="form_255.png"> of the process after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_245.png"> according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
<p>
Reimplemented in <a class="el" href="class_quant_lib_1_1_hull_white_process.html#5da3e29d59b0c10b20f760739de77535">HullWhiteProcess</a>, <a class="el" href="class_quant_lib_1_1_hull_white_forward_process.html#5da3e29d59b0c10b20f760739de77535">HullWhiteForwardProcess</a>, and <a class="el" href="class_quant_lib_1_1_ornstein_uhlenbeck_process.html#5da3e29d59b0c10b20f760739de77535">OrnsteinUhlenbeckProcess</a>.
</div>
</div><p>
<a class="anchor" name="096b196eb0c6e453acbd428ae378c7de"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::evolve" ref="096b196eb0c6e453acbd428ae378c7de" args="(Time t0, Real x0, Time dt, Real dw) const" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">virtual Real evolve </td>
<td>(</td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>t0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Real </td>
<td class="paramname"> <em>x0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Time </td>
<td class="paramname"> <em>dt</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Real </td>
<td class="paramname"> <em>dw</em></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const<code> [virtual]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>
returns the asset value after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_245.png"> according to the given discretization. By default, it returns <p class="formulaDsp">
<img class="formulaDsp" alt="\[ E(x_0,t_0,\Delta t) + S(x_0,t_0,\Delta t) \cdot \Delta w \]" src="form_256.png">
<p>
where <img class="formulaInl" alt="$ E $" src="form_249.png"> is the expectation and <img class="formulaInl" alt="$ S $" src="form_135.png"> the standard deviation.
</div>
</div><p>
<a class="anchor" name="6c8e95cb5b48a9ca86fef990c92c58c9"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::apply" ref="6c8e95cb5b48a9ca86fef990c92c58c9" args="(Real x0, Real dx) const" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">virtual Real apply </td>
<td>(</td>
<td class="paramtype">Real </td>
<td class="paramname"> <em>x0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Real </td>
<td class="paramname"> <em>dx</em></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const<code> [virtual]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>
applies a change to the asset value. By default, it returns <img class="formulaInl" alt="$ x + \Delta x $" src="form_257.png">.
<p>
Reimplemented in <a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#181565755d35d36c7bf732e1905f3661">GeneralizedBlackScholesProcess</a>, and <a class="el" href="class_quant_lib_1_1_merton76_process.html#80c11f9def74e04938f4c2319722c37c">Merton76Process</a>.
</div>
</div><p>
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